Laws of Motion JEE Advanced previous year questions with solutions

5 solved JEE Advanced questions on Laws of Motion, free to read — no sign-in needed. The full chapter has 30 questions; sign in to attempt the remaining 25 in the exam simulator.

1. Q1JEE Advanced Adv 2025 (Paper 1)
   A person sitting inside an elevator performs a weighing experiment with an object of mass 50 kg . Suppose that the variation of the height $y$ (in m ) of the elevator, from the ground, with time $t$ (in s ) is given by $y=8\left[1+\sin \left(\frac{2 \pi t}{T}\right)\right]$, where $T=40 \pi \mathrm{~s}$. Taking acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^2$, the maximum variation of the object's weight (in N ) as observed in the experiment is _______ .
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   Answer: 2

   $y=8+8 \sin \frac{2 \pi t}{T}$ With respect to elevator, variation in weight will be $\begin{aligned} & \Delta \mathrm{W}=\mathrm{m}(\Delta \mathrm{a})_{\max } \\ & \Delta \mathrm{W}=\mathrm{m} \times 2 \omega^2 \mathrm{~A}\end{aligned}$ Here elevator is performing SHM $\begin{aligned} & \Delta \mathrm{W}=2 \mathrm{~m} \times\left(\frac{2 \pi}{\mathrm{~T}}\right)^2 \times \mathrm{A} \mathrm{N} \\ & \Delta \mathrm{W}=2 \times 50 \times\left(\frac{2 \pi}{40 \pi}\right)^2 \times 8 \mathrm{~N} \\ & \Delta \mathrm{~W}=2 \times 50 \times \frac{1}{400} \times 8 \mathrm{~N} \\ & \Delta \mathrm{~W}=\frac{800}{400} \mathrm{~N}=2 \mathrm{~N}\end{aligned}$
2. Q2JEE Advanced Adv 2018 (Paper 2)
   A particle, of mass ${10}^{-3}kg$ and charge $1.0C$, is initially at rest. At time $t=0$, the particle comes under the influence of an electric field $\vec{E}\left(t\right)={E}_{0}\sin \left(\omega t\right)\hat{i}$ where ${E}_{0}=1.0N{C}^{-1}$ and $\omega ={10}^{3}rad{s}^{-1}$. Consider the effect of only the electrical force on the particle. Then the maximum speed, in $m{s}^{-1}$, attained by the particle at subsequent times is ____________.
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   Answer: 2

   $m={10}^{-3}kg,q=1C,t=0$ Force on particle will be $F=qE=q{E}_{0}\sin \left(\omega t\right)$ At ${v}_{max},F=0$ $\Rightarrow q{E}_{0}\sin ⁡\omega {t}_{o}=0$ $\Rightarrow \omega {t}_{o}=\pi$ $F=q{E}_{0}\sin ⁡\omega t$ $\dfrac{dv}{dt}=q\dfrac{{E}_{0}}{m}\sin \left(\omega t\right)$ ${\int }_{0}^{v}dv={\int }_{0}^{\pi ∕\omega }\dfrac{q{E}_{0}}{m}\sin \left(\omega t\right)dt$ $v-0=\dfrac{q{E}_{0}}{m\omega }{\left[-\cos \left(\omega t\right)\right]}_{0}^{\pi ∕\omega }$ $v-0=\dfrac{q{E}_{0}}{m\omega }\left[\left(-\cos \left(\pi \right)\right)-\left(-\cos \left(0\right)\right)\right]$ $v=\dfrac{1\times 1}{m\omega }\times 2=2m{s}^{-1}$
3. Q3JEE Advanced Adv 2018 (Paper 2)
   A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the x - axis. Its kinetic energy changes with time as $dK/dt=\gamma t,$ where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?
   1. A.The force applied on the particle is constant
   2. B.The speed of the particle is proportional to time
   3. C.The distance of the particle from the origin increases linearly with time
   4. D.Since force is constant, it is conservative.
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   Answer: A,B,D

   Given the change in kinetic energy$\dfrac{dk}{dt}=\gamma t$. Kinetic energy is expressed as $k=\dfrac{1}{2}m{v}^{2}$. $∴\dfrac{dk}{dt}=mv\dfrac{dv}{dt}=\gamma t$ Integrating the above relation, $m{\int }_{0}^{v}vdv=\gamma {\int }_{0}^{t}tdt$ $\dfrac{m{v}^{2}}{2}=\dfrac{\gamma {t}^{2}}{2}$ $v=\sqrt{\dfrac{\gamma }{m}}t;υ\propto t$ ... (i) $a=\dfrac{dv}{dt}=\sqrt{\dfrac{\gamma }{m}}=constant$ Since $F=ma$ $∴F=m\sqrt{\dfrac{\gamma }{m}}=\sqrt{\gamma m}=constant$
4. Q4JEE Advanced Adv 2008 (Paper 2)
   Statement 1 It is easier to pull a heavy object than to push it on a level ground. and Statement 2 The magnitude of frictional force depends on the nature of the two surfaces in contact.
   1. A.Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
   2. B.Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
   3. C.Statement 1 is true, Statement 2 is false.
   4. D.Statement 1 is false, Statement 2 is true
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   Answer: (B)

   Both statements are correct. But statement-2, does not explain correctly, statement- 1 . Correct explanation is : "There is increase in nomal reaction when the object is pushed and there is decrease in normal reaction when the object is pulled (but strictly not horizontally).
5. Q5JEE Advanced Adv 2007 (Paper 2)
   Statement I A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table. Statement II For every action there is an equal and opposite reaction.
   1. A.Statement I is true, Statement II is true; Statement II is a correct explanation for Statement.
   2. B.Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I
   3. C.Statement I is true, Statement II is false
   4. D.Statement I is false, Statement II is true
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   Answer: (B)

   The cloth can be pulled out without dislodging the dishes from the table due to law of inertia, which is Newton's first law. While the Statement II is true, but it is Newton's third law. $\therefore$ Correct option is (b).